Thermal-chemical simulation method for composite material curing based on physical information neural network

Abstract

The invention discloses a thermal-chemical simulation method for composite material curing based on a physical information neural network, and the method comprises the steps: constructing a composite material curing thermal-chemical coupling neural network which comprises an attention mechanism and a multi-scale network structure, and is used for extracting and fusing temperature fields and curing degree features of different scales; embedding the temperature field Fourier heat conduction control equation, the curing degree aesthetic dynamics model and the stress-strain relation equation into a loss function of the coupling neural network to form a comprehensive loss function, and dynamically adjusting a weight coefficient of a physical equation through a curing progress to obtain a stress-strain coefficient of the coupling neural network; enhancing the description capability of the coupling neural network on the multi-physics field coupling behavior in the curing process; training the coupled neural network by adopting an improved AdamW optimization algorithm in combination with a cosine annealing learning rate strategy; and verifying and optimizing the coupled neural network in actual production, and introducing relative error and root-mean-square error indexes to evaluate the precision of the neural network.

Description

Technical Field

[0001] The present invention relates to a thermal-chemical simulation method for composite material curing based on a physics-informed neural network. Background Art

[0002] In the early stage, an approximate prediction of the composite material curing process was established through a neural network, which could only learn and predict through a large amount of data. And if the structure was changed, data samples were usually difficult to obtain, and the prediction accuracy depended on the data accuracy, but the calculation efficiency was high. Recently, physical information was combined as a loss with a convolutional neural network for unsupervised learning to simulate the thermal-chemical process of the composite material curing process, and the temperature and degree of cure at any time and any position could be accurately simulated. However, the network adopted a point-to-point mapping form and the calculation efficiency was lower than that of traditional finite element calculations. Summary of the Invention

[0003] The present invention provides a thermal-chemical simulation method for composite material curing based on a physics-informed neural network to solve the problems existing in the above-mentioned prior art.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A thermal-chemical simulation method for composite material curing based on a physics-informed neural network (PINN) includes the following steps:

[0006] S1: Construct a thermal-chemical coupling neural network for composite material curing including an attention mechanism and a multi-scale network structure to extract and fuse temperature field and degree of cure characteristics at different scales;

[0007] S2: Embed the temperature field Fourier heat conduction control equation, the degree of cure phenomenological kinetics model, and the stress-strain relationship equation into the loss function of the coupling neural network to form a comprehensive loss function, and dynamically adjust the weight coefficients of the physical equations according to the curing progress to enhance the description ability of the coupling neural network for the multi-physical field coupling behavior during the curing process;

[0008] S3: Train the coupling neural network using an improved AdamW optimization algorithm combined with a cosine annealing learning rate strategy;

[0009] S4: Verify and optimize the coupling neural network in actual production, and introduce relative error and root mean square error indicators to evaluate the accuracy of the neural network.

[0010] 2. The thermal-chemical simulation method for composite material curing based on a physics-informed neural network according to claim 1, wherein in S1, the calculation formula for the attention weight in the attention mechanism is:

[0011]

[0012] Among them: α i represents the attention weight at the i-th position, W a and b a are the weight matrix and bias term of the attention mechanism respectively, used to learn the importance of features at different positions; f i is the feature vector at the i-th position, and n is the total number of feature vectors.

[0013] By calculating the weights of features at each position, this formula enables the network to automatically focus on the key areas during the curing process of the composite material, improving the model's ability to capture important physical phenomena.

[0014] Furthermore, in S1, in the multi-scale network structure, the formula for extracting the temperature field features at the k-th scale is:

[0015] T(k) = Conv scale-k (T input )

[0016] Among them, T (k) represents the temperature field features extracted at the k-th scale, Conv scale-k is the convolution operation at the k-th scale, used to extract temperature information at different scales; T input is the input temperature field data;

[0017] The feature fusion formula is:

[0018]

[0019] Among them, T fuse and C fuse are the fused temperature field and cure degree features respectively, W k and b fuse are the weight matrix and bias term of the fusion layer, used to perform weighted fusion on features at different scales; m is the number of scales. Through multi-scale feature extraction and fusion, the complex physical phenomena during the curing process of the composite material can be characterized more comprehensively.

[0020] Furthermore, in S2, the comprehensive loss function is:

[0021]

[0022] Among them, is the comprehensive loss function; is the loss of the temperature field physical equation; is the loss of the cure degree phenomenological kinetics model; is the loss of the stress-strain relationship equation; λ is the weight coefficient.

[0023] Furthermore, in S2, the formula for calculating the curing progress index is:

[0024]

[0025] Among them, C(x, t) is the degree of cure at position x and time t, and C max is the maximum degree of cure, and V is the volume of the composite material;

[0026] The formula for dynamically adjusting the weight coefficient is:

[0027]

[0028] Among them, λ(t) is the weight coefficient at time t, λ0 is the initial weight coefficient, and p max is the maximum curing progress.

[0029] By dynamically adjusting the weight coefficient of the physical equation, the curing thermo-chemical coupling neural network of the composite material can better adapt to the actual physical process at different curing stages, improving the accuracy and efficiency of the simulation.

[0030] Furthermore, in S3, improving the AdamW optimization algorithm is to improve the weight decay in the original AdamW optimization algorithm, and the improved formula is:

[0031]

[0032] Among them, w t+1 is the model weight at time step t + 1, and w t is the model weight at time step t; η is the learning rate, controlling the step size of parameter update;

[0033] is the gradient of the loss function, indicating the direction of parameter update; v t is the exponentially weighted average of the squared gradient, used to adaptively adjust the learning rate; ∈ is a numerical stability term to prevent the denominator from being zero;

[0034] The formula for adjusting the learning rate is:

[0035]

[0036] Among them, η t is the learning rate at time step t, η max is the maximum learning rate, and T is the learning rate adjustment period.

[0037] By improving the optimization algorithm, the training speed of the curing thermo-chemical coupling neural network of the composite material can be accelerated, and its convergence performance and generalization ability can be improved.

[0038] Furthermore, in S4, the calculation formula for the relative error index adopted is:

[0039]

[0040] Among them, Relative Error is the relative error, which measures the relative deviation between the predicted value of the model and the calculated value by the finite element method; y PINN is the prediction result of the coupled neural network, and yFEM is the calculation result by the finite element method;

[0041] The calculation formula for the root mean square error index is:

[0042]

[0043] Among them, RMSE is the root mean square error, which is used to evaluate the average difference degree between the predicted value of the model and the calculated value by the finite element method; N is the number of data points, y PINN,i and y FEM,i are the predicted values of the coupled neural network and the finite element method at the i-th data point, respectively.

[0044] By introducing a variety of verification indicators, the accuracy and reliability of the composite material curing thermo-chemical coupled neural network can be evaluated more comprehensively, providing a strong basis for the optimization of the model.

[0045] Furthermore, the expression of the kernel integral operator of the coupled neural network is:

[0046]

[0047] Among them, the input function v i (x, t) of the i-th Fourier layer undergoes Fourier kernel integral transformation and is connected to the spatial convolution operator W, and after passing through the activation function σ, the output function v i+1 (x, t) of the i-th Fourier layer is obtained.

[0048] The present invention has the following beneficial effects:

[0049] By integrating the physics-informed neural network with the composite material curing simulation, the simulation accuracy and efficiency are innovatively improved, and it has patentability. By dynamically adjusting the weight coefficients and introducing a variety of verification indicators, the curing process is accurately simulated to ensure reliable results. The improved optimization algorithm and efficient network structure improve the calculation efficiency and meet the actual production requirements. The multi-scale network structure and dynamic weight adjustment comprehensively consider the multi-physics field coupling behavior and adapt to different process conditions. Description of the Drawings

[0050] Figure 1 This is a comparison of the finite element and PINN temperatures and degrees of cure at the center point of the 10mm laminate of the present invention.

[0051] Figure 2Comparison of finite element and PINN calculation results for the 10mm laminate of the present invention.

[0052] Figure 3 Comparison of finite element and PINN temperature and degree of cure for the center point of the 20mm laminate of the present invention.

[0053] Figure 4 Comparison of finite element and PINN calculation results for the 20mm laminate of the present invention.

[0054] Figure 5 Comparison of finite element and PINN temperature and degree of cure for the center point of the 30mm laminate of the present invention.

[0055] Figure 6 Comparison of finite element and PINN calculation results for the 30mm laminate of the present invention. Detailed implementation manners

[0056] The present invention will be further described below with reference to the accompanying drawings.

[0057] A thermal-chemical simulation method for composite material curing based on a physics-informed neural network (PINN) of the present invention includes the following steps:

[0058] S1: Construct a thermal-chemical coupling neural network for composite material curing including an attention mechanism and a multi-scale network structure, for extracting and fusing temperature field and degree of cure features at different scales;

[0059] S2: Embed the Fourier heat conduction control equation of the temperature field, the phenomenological kinetics model of the degree of cure, and the stress-strain relationship equation into the loss function of the coupling neural network to form a comprehensive loss function, and dynamically adjust the weight coefficients of the physical equations according to the curing progress to enhance the description ability of the coupling neural network for the multi-physical field coupling behavior during the curing process;

[0060] S3: Train the coupling neural network using an improved AdamW optimization algorithm combined with a cosine annealing learning rate strategy;

[0061] S4: Verify and optimize the coupling neural network in actual production, and introduce relative error and root mean square error indicators to evaluate the accuracy of the neural network.

[0062] In S1, the calculation formula for the attention weight in the attention mechanism is:

[0063]

[0064] Where: α i represents the attention weight at the i-th position, W a and b a are the weight matrix and bias term of the attention mechanism respectively, for learning the importance of features at different positions; fi is the feature vector at the i-th position, and n is the total number of feature vectors.

[0065] By calculating the weights of the features at each position, this formula enables the network to automatically focus on the key areas during the curing process of the composite material, enhancing the model's ability to capture important physical phenomena.

[0066] In the multi-scale network structure, the formula for extracting the temperature field features at the k-th scale is:

[0067] T (k) = Conv scale-k (T input )

[0068] where T (k) represents the temperature field features extracted at the k-th scale, Conv scale-k is the convolution operation at the k-th scale, used to extract temperature information at different scales; T input is the input temperature field data;

[0069] The feature fusion formula is:

[0070]

[0071] where T fuse and C fuse are the fused temperature field and degree of cure features respectively, W k and b fuse are the weight matrix and bias term of the fusion layer, used to perform weighted fusion on features at different scales; m is the number of scales. Through multi-scale feature extraction and fusion, the complex physical phenomena during the curing process of the composite material can be characterized more comprehensively.

[0072] In S2, the comprehensive loss function is:

[0073]

[0074] where is the comprehensive loss function; is the loss of the temperature field physical equation; is the loss of the degree of cure phenomenological kinetic model; is the loss of the stress-strain relationship equation; λ is the weight coefficient.

[0075] The formula for calculating the index of the curing progress is:

[0076]

[0077] where C(x,t) is the degree of cure at position x at time t, C max is the maximum degree of cure, and V is the volume of the composite material;

[0078] The dynamic adjustment formula of the weight coefficient is as follows:

[0079]

[0080] Among them, λ(t) is the weight coefficient at time t, λ0 is the initial weight coefficient, and p max is the maximum curing progress. By dynamically adjusting the weight coefficient of the physical equation, the curing thermo-chemical coupling neural network of the composite material can better adapt to the actual physical process at different curing stages, improving the accuracy and efficiency of the simulation.

[0081] The expression of the kernel integral operator of the coupled neural network is:

[0082]

[0083] Among them, the input function v i (x, t) of the i-th Fourier layer undergoes Fourier kernel integral transform and is connected to the spatial convolution operator W, and after passing through the activation function σ, the output function v i+1 (x, t) of the i-th Fourier layer is obtained.

[0084] Through the kernel integral operator, the curing process temperature is subjected to fast Fourier transform, low-frequency filtering, linear transformation, inverse fast Fourier transform, and non-linear activation, and then the temperature and curing degree at any time inside the composite material are output, thereby realizing the mapping from function to function. Compared with the point-to-point mapping, the efficiency of calculating the curing of the composite material using the kernel integral operator is increased by more than 10 times.

[0085] In S3, the improved AdamW optimization algorithm improves the weight decay in the original AdamW optimization algorithm, and the improved formula is:

[0086]

[0087] Among them, w t+1 is the model weight at time step t + 1, and w t is the model weight at time step t; η is the learning rate, which controls the step size of parameter update;

[0088] is the gradient of the loss function, indicating the direction of parameter update; v t is the exponentially weighted average of the squared gradient, used to adaptively adjust the learning rate; ∈ is the numerical stability term to prevent the denominator from being zero;

[0089] The learning rate adjustment formula is:

[0090]

[0091] Among them, η t is the learning rate at time step t, η max is the maximum learning rate, and T is the learning rate adjustment period.

[0092] By improving the optimization algorithm, the training speed of the thermo-chemical coupling neural network for the curing of the composite material can be accelerated, and its convergence performance and generalization ability can be improved.

[0093] In S4, the calculation formula for the relative error index adopted is:

[0094]

[0095] Among them, Relative Error is the relative error, which measures the relative deviation between the predicted value of the model and the calculated value by the finite element method; y PINN is the prediction result of the coupling neural network, and yFEM is the calculation result by the finite element method;

[0096] The calculation formula for the root mean square error index is:

[0097]

[0098] Among them, RMSE is the root mean square error, which is used to evaluate the average difference degree between the predicted value of the model and the calculated value by the finite element method; N is the number of data points, and y PINN,i and y FEM,i are respectively the predicted values of the coupling neural network and the finite element method at the i-th data point. By introducing multiple verification indicators, the accuracy and reliability of the thermo-chemical coupling neural network for the curing of the composite material can be evaluated more comprehensively, providing a strong basis for the optimization of the model.

[0099] Figures 1 to 6 Models with three different thicknesses of 10mm, 20mm, and 30mm are established respectively. Through comparison, it can be seen that the accuracy is excellent and the calculation efficiency is higher than that of the finite element method.

[0100] The above is only the preferred implementation manner of the present invention. It should be noted that for those of ordinary skill in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A thermo-chemical simulation method for curing composite materials based on a physics-informed neural network, characterized in that: It includes the following steps: S1: Construct a composite material curing thermo-chemical coupling neural network including an attention mechanism and a multi-scale network structure to extract and fuse temperature field and curing degree characteristics at different scales; S2: Embed the temperature field Fourier heat conduction control equation, the phenomenological kinetics model of curing degree, and the stress-strain relationship equation into the loss function of the coupling neural network to form a comprehensive loss function, and dynamically adjust the weight coefficients of the physical equations according to the curing progress to enhance the description ability of the coupling neural network for the multi-physical field coupling behavior during the curing process; S3: Train the coupling neural network using an improved AdamW optimization algorithm combined with a cosine annealing learning rate strategy; S4: Verify and optimize the coupling neural network in actual production, and introduce relative error and root mean square error indicators to evaluate the accuracy of the neural network.

2. The thermo-chemical simulation method for composite material curing based on the physics-informed neural network according to claim 1, wherein: In S1, the calculation formula for the attention weight in the attention mechanism is: Where: α i represents the attention weight at the i-th position, W a and b a are the weight matrix and bias term of the attention mechanism respectively, used to learn the importance of features at different positions; f i is the feature vector at the i-th position, and n is the total number of feature vectors.

3. The thermo-chemical simulation method for composite material curing based on the physics-informed neural network according to claim 1, characterized in that: In S1, in the multi-scale network structure, the formula for extracting the temperature field characteristics of the k-th scale is: T (k) = Conv scale-k (T input ) Among them, T (k) represents the temperature field feature extracted at the k-th scale, and Conv scale-k is the convolution operation at the k-th scale, which is used to extract temperature information at different scales; T input is the input temperature field data; The feature fusion formula is: Among them, T fuse and C fuse are respectively the fused temperature field and the degree of curing characteristics, W k and b fuse are the weight matrix and bias term of the fusion layer, which are used to perform weighted fusion on features of different scales; m is the number of scales.

4. The thermo-chemical simulation method for composite material curing based on the physics-informed neural network according to claim 1, characterized in that: In S2, the comprehensive loss function is: Among them, is the comprehensive loss function; is the loss of the physical equation of the temperature field; is the loss of the phenomenological kinetics model of the degree of curing; is the loss of the stress-strain relationship equation; λ is the weight coefficient.

5. The thermo-chemical simulation method for composite material curing based on the physics-informed neural network according to claim 4, characterized in that: In S2, the calculation formula for the index of the curing progress is: where C(x, t) is the degree of cure at position x and time t, and C max is the maximum degree of cure, and V is the volume of the composite material; The dynamic adjustment formula for the weight coefficient is: where λ(t) is the weight coefficient at time t, λ0 is the initial weight coefficient, and p max is the maximum curing progress.

6. The thermo-chemical simulation method for curing composite materials based on the physics-informed neural network according to claim 5, wherein: In S3, the improved AdamW optimization algorithm improves the weight decay in the original AdamW optimization algorithm, and the improved formula is: where, w t+1 is the model weight at time step t+1, and w t is the model weight at time step t; η is the learning rate, which controls the step size of parameter update; is the gradient of the loss function; v t is the exponentially weighted average of the squared gradient; ∈ is the numerical stability term; The learning rate adjustment formula is: Among them, η t is the learning rate at time step t, η max is the maximum learning rate, and T is the learning rate adjustment period.

7. The thermo-chemical simulation method for curing composite materials based on physics-informed neural networks according to claim 5, characterized in that: In S4, the calculation formula for the relative error indicator used is: Among them, Relative Error is the relative error; y PINN is the prediction result of the coupled neural network, and yFEM is the calculation result of the finite element method; The root mean square error indicator calculation formula is: where RMSE is the root mean square error; N is the number of data points, and y PINN,i and y FEM,i are the predicted values of the coupled neural network and the finite element method at the i-th data point, respectively.

8. The thermal-chemical simulation method for composite material curing based on physics-informed neural network according to claim 1, characterized in that: The expression of the kernel integral operator of the coupling neural network is: Among them, the input function v of the i-th Fourier layer i (x, t) undergoes a Fourier kernel integral transform and is connected to the spatial convolution operator W. After passing through the activation function σ, the output function v of the i-th Fourier layer is obtained i+1 (x, t).

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